Market demand is given by P = 15 - Q. There are two firms, each with TC = 0.5q_i². If one firm honors the cartel agreement while the other firm defects, the output produced by the defecting firm is: A)2. B)4. C)8. D)12.

Question

Quizplus · Accepted Answer

The cartel agreement means that both firms collude to maximize their joint profit. To find the profit-maximizing output for each firm, we need to find the point where their marginal cost (MC) equals the market price.
MC for each firm can be found by taking the derivative of their total cost (TC) function:
MC = d(TC)/dq = 0.5
Setting MC = P, we get:
0.5 = 15 - Q
Q = 14.5
So the profit-maximizing output for each firm under the cartel agreement is Q = 7.25.
If one firm defects and produces more than 7.25 units, its profit will increase because it can charge a higher price due to the lower total output in the market. The other firm would still produce 7.25 units, since that is its profit-maximizing output under the cartel agreement.
So the output produced by the defecting firm would be:
Q_defecting = Q_market - Q_honoring
Q_defecting = 15 - Q_honoring - Q_honoring (since there are two firms)
Q_defecting = 15 - 2(7.25)
Q_defecting = 0.5
Therefore, the answer is B) 4.

Market Demand Is Given by P = 15 - Q